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Unformatted text preview: ECE 495N EXAM II
CLOSED BOOK Wednesday, N0v.5, 2008 NAME : PUID # : Please Shaw all work and write Yﬂur answers clearly.
This exam should have seven pages. Problem 1 [11. 2, 3] 8 points
Problem 2 [1}. 4, 5] 9 points
Problem 3 [p. 6, T] 8 points
Total 25 points
Useful Relations:
1
f(EJ = ——— Fermi ﬁmcn‘an 1+:xpiE— “MET pa .= % app. ( .15".z _ my“ )fkT) Law of equilibrium [Mk3]: E[Hm]exp(flév(ém—&n)) Bandsimcmre D(E)  E 6(E — 50%)) Emmy of Emma
k O a E
M(EJ= 2&(E—smnw Densiw of modes a item?)
“(m a dual Problem 1: A channel has twe energy levels with the same energy,r e , but the
interaction energyr is an high that me more than ene of these levels can he eeeupied
at the same time. What is. the average number of eleetrene in the channel if it is in
equiiibrium with chemical petential a and temperature T? Yeur answer sheuld he in terms of 5,}: and T. Problem 2: Benmene molecule consists of six carbon atoms arranged at the corners of a
regular hexagon of side ‘a’. Assume (I) one orbital per carbon atom as basis ﬁmetion ;
(2) the overlap matrix [S] is a (6x6) identity matrix; and (3} the Hamiltonian matrix is
given by Hm = e (site energy) H n m = r if n, m are neighboring atoms H" m = ﬂ ifn, m are NOT nearest neighbors (a) What are the six energy eigenvalues in terms of ‘ s’ and ‘t’? <__ a n} (b) What are the corresponding eigenveetors? Problem 3: Suppese a large two—dimensional eendueter has an sUE) relationship given by: as; = Aka where A is a constant and k2 = k: + k3. Derive an expression fer the density of states, D{E}.
Your answer should he in terms of the energjj.f E, A, width W and length L. ...
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This note was uploaded on 12/30/2010 for the course ECE 495N taught by Professor S.datta during the Spring '08 term at Indiana UniversityPurdue University Fort Wayne.
 Spring '08
 S.Datta

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